The circuit uses the popular LM324 op-amp to create a current and voltage limited power supply. In this case, the current is adjustable with a potentiometer from about 160 to 1600mA, making it able to charge batteries with a wide range of capacities. The voltaje limit is 4.2v, so you don't damage your batteries. It has a charge indicator LED that will lit up while the battery is charging and shut off when done. I designed this circuit so it uses widely available and cheap through-hole components so anyone can build it. Almost any general purpose op-amp can be used, no rail to rail operation needed, no high frequency or precision. The tip122 transistors can be replaced with any pin-compatible transistor with a minimum DC current gain (Hfe) over 100 and a maximum collector current (Ic) over 2A. As a first test, i'm goung to charge a 600mAh battery, i'm goung to charge it at 0.5C to be safe. First of all, connect your multimeter to the output and set the dial to current in the 10A range. Plug the charger and turn the potentiometer until the output current is half the nominal capacity of the battery, in my case, 0.3A. Then, connect the battery to the charger, and be careful with the polarity, in my circuit design, the positive pin is on the right of the connectors. I tested the 4.2v reference below VCC, and as you can se in the pictures, it's a perfect 4.2v reference. When i began to charge the battery, it had an open circuit voltage of 3.1v, so pretty empty. About an hour and a half later, the battery had a voltage of 4.09v, it was about to enter in the constant voltage stage. An hour and a half later, i saw the LED was dimming out, so i checked the current via the voltage drop across the sense resistor, the current was about 24mA, which is less than 9% of the initial 300mA. At that point the battery was completely charged. This charger works great, i've tested it with that 600mAh battery, a 840mAh DSI battery, a little 200mAh watch battery and a 4000mAh tablet battery. They all took around 3 hours to fully charge, the 4Ah one took a bit longer, but just because the charger is limited to 1.6A, and that's a 0.4C charge rate.